Question

Which point could be on the line that is perpendicular to and passes through point K?

Answer 1

It would be (2,2), because of the opposite reciprocal slope of a perpendicular line.

Answer 2

Answer:

(2, 2)

Step-by-step explanation:

First we find the slope of the line through M and N.  The coordinates of M are (2, 3) and the coordinates of N are (-3, 2).  Using the formula for slope,

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{2--3}=\frac{1}{5}$

For a line to be perpendicular to a given line, the slopes would be negative reciprocals (opposite signs and the fraction is flipped).  This makes the slope of the perpendicular line -5/1.

The coordinates of point K are (3, -3).  Going down 5 units and right 1 unit would put it at (4, -8).  Going backwards, up 5 units and left 1 unit would be (2, 2).  Thus (2, 2) is the point we are looking for.